Programmation lin\303\251aireAndr\303\251 L\303\251vesque
Cette application permet d'optimiser une fonction lin\303\251aire \303\240 deux variables ou plus. Lorsque le probl\303\250me est \303\240 deux ou trois variables, l'application localise dans le plan cart\303\251sien ou dans un espace \303\240 trois dimensions, l'ensemble convexe des solutions r\303\251alisables du probl\303\250me ainsi que tous ses sommets. Pour lancer l'application, cliquez sur !!! ou choississez Edit -> Execute -> Worksheet. ou placez votre curseur sur une ligne rouge du programme puis cliquez sur la touche retour.
**************************************restart:
_t:=NULL:
dStandard := proc(r1)
local coord, xmin, xmax, ymin, ymax, eq, g, g1, g2, A, B, X, Y, c, h, i, j, k, l, cv, cs, ct, p, s, d, v1, v2, _C, _w:
global _cnsts, _obj, s_opt, _var, _nc, _nv, x, y, z, _sr, _t:
use Maplets[Tools] in
x:='x': y:='y': z:='z':
_cnsts:={}:
if Get('TF0')="" or Get('TF1')="" then
return(plot(0,x=1..2,1..2, axes=NONE))
else
_obj:=Get('TF0'::algebraic):
d:=Get('TF1')
fi:
_cnsts:="":
k:="":
j:="":
if d[length(d)]<>"\134n" then d:=cat(d,"\134n") fi:
for i from 1 to length(d) do
if d[i]<>"\134n" then
j:=cat(convert(j,string),convert(d[i],string)):
_cnsts:=cat(convert(_cnsts,string),convert(d[i],string))
elif d[i]="\134n" and k<>"\134n" and i<>1 then
Set('TBX'=j):
Get('TBX'::{'`<=`','`=`'}):
j:="":
_cnsts:=cat(convert(_cnsts,string),convert(",",string)):
fi:
k:=d[i]
od:
if _cnsts[length(_cnsts)]="," then
_cnsts:=cat(seq(_cnsts[j], j=1..length(_cnsts)-1)):
fi:
_cnsts:=simplex[standardize](convert({parse(_cnsts)},rational)):
_nc:=[]:
_nv:=[]:
cv:=_cnsts union {_obj}:
for i from 1 to nops(cv) do
if nops(op([i],cv))=2 then
cs:=op([i,1],cv)-op([i,2],cv):
else
cs:=op([i],cv):
fi:
for j from 1 to nops(cs) do
for k from 1 to nops(op([j],cs)) do
if is(op([j,k],cs),numeric)=false then
ct:=convert(op([j,k],cs),string):
_nv:=[op(_nv),ct]:
fi:
od:
od:
_nc:=[op(_nc),op(_nv)]:
_nv:=[]:
od:
_var:=[]:
for i from 1 to nops(_obj) do
for j from 1 to nops(op(i,_obj)) do
if is(op(j,op(i,_obj)),name)=true then
_var:=[op(_var),convert(op(j,op(i,_obj)),string)]
fi
od
od:
k:=convert(_nc,set) minus convert(_var,set):
for i from 1 to nops(k) do
_var:=[op(_var),op(i,k)]:
od:
_nv:=nops(convert(_nc,set)):
if _obj<>"" and not(is(_obj<infinity)) then
if r1=true then
s_opt:=simplex[minimize](_obj,_cnsts,NONNEGATIVE):
else
s_opt:=simplex[maximize](_obj,_cnsts,NONNEGATIVE):
fi:
if _nv=2 then
x:='x': y:='y': z:='z':
for i from 1 to 2 do
if _var[i]="x" then
_var[i]:=_var[1]:
_var[1]:="x"
elif _var[i]="y" then
_var[i]:=_var[2]:
_var[2]:="y"
fi
od:
x:=parse(op(1,_var)):
y:=parse(op(2,_var)):
_cnsts := _cnsts union { x >= 0, y >= 0 }:
if s_opt<>{} then
eq:=seq(op(_cnsts[i])[1]=op(_cnsts[i])[2],i=1..nops(_cnsts)):
X:=[]:
Y:=[]:
for i from 1 to nops({eq})-1 do
for j from i+1 to nops({eq}) do
p:=solve({eq[i],eq[j]}):
s:=subs(p,_cnsts):
k:=0:
for l from 1 to nops(s) do
if evalb(s[l])=true then
k:=k+1
fi
od:
if k=nops(s) then
if op(p[1])[1]=x then
X:=[op(X),op(p[1])[2]]: Y:=[op(Y),op(p[2])[2]]
else
X:=[op(X),op(p[2])[2]]: Y:=[op(Y),op(p[1])[2]]
fi:
fi:
od:
od:
xmax:=1.25*max(op(X));
ymax:=1.25*max(op(Y));
if xmax=0 then
xmax:=10
fi:
if ymax=0 then
ymax:=10
fi:
fi;
if s_opt={} then
xmax:=10:
ymax:=10
fi:
xmin:=(-1)*xmax/6:
ymin:=(-1)*ymax/6:
g1:=plots[inequal](_cnsts, x = xmin .. xmax, y = ymin .. ymax, optionsfeasible = (color = grey), optionsclosed = (color = black, thickness = 1), optionsexcluded = (color = white),tickmarks=[3,3], labels=[x, y]):
if s_opt<>{} and s_opt<>NULL then
g2:=plots[implicitplot](_obj=subs(s_opt,_obj), x=xmin..xmax, y=ymin.. ymax, thickness = 2, linestyle=1, color=green, labels=[x, y]):
if op(s_opt[1])[1]=x then
coord:=[op(s_opt[1])[2],op(s_opt[2])[2]]
else
coord:=[op(s_opt[2])[2],op(s_opt[1])[2]]
fi:
_w:=subs({x=coord[1],y=coord[2]},_obj):
k:=0:
_C:=[]:
for i from 1 to nops(X) do
_C:=[op(_C), [X[i],Y[i]]]:
_C:=[op({op(_C)})]:
if subs({x=op(X(i))[i],y=op(Y(i))[i]},_obj)=_w then
k:=k+1: c[k]:=[op(X(i))[i],op(Y(i))[i]]
fi:
od;
for i from 1 to nops(_C) do
l:=_C[i]:
for j from i+1 to nops(_C) do
if op(_C)[j,1]<op(_C)[i,1] then
l:=_C[j]: _C[j]:=_C[i]: _C[i]:=l
fi:
od:
od:
c:={seq(c[i],i=1..k)}:
if nops(c)<=1 then
for i from 1 to nops(_C) do
k:=0:
for j from nops(_C) to i+1 by -1 do
if abs(_C[i,1]-_C[j,1])/(xmax-xmin)< (length(cat(convert(_C[i,1],string), convert(_C[i,2],string)))+3)/60 and abs(_C[i,2]-_C[j,2])/(ymax-ymin)<0.05 then
k:=k+1:
fi:
od:
if _C[i,2]=0 and k=0 then
A:={ABOVE,RIGHT}:
else
if _C[i,2]=0 and k>0 then
A:={BELOW,RIGHT}:
else
if k=0 then
A:={ABOVE,RIGHT}:
else
A:={ABOVE,LEFT}:
fi:
fi:
fi:
if r1=true then
B:="minimale"
else
B:="maximale"
fi:
g[i]:=plots[textplot]([_C[i,1],_C[i,2],cat(" (",convert(_C[i,1],string),", ",convert(_C[i,2],string),") ")],align=A):
_t:=cat(`La valeur `, B, ` de la fonction objectif est `, convert(parse(convert(_w,CaractDec)),string), ` lorsque `, convert(x,string), `=`, convert(coord[1],string), ` et `, convert(y, string), `=`, convert(coord[2],string)):
od:
else
for i from 1 to nops(_C) do
k:=0:
for j from nops(_C) to i+1 by -1 do
if abs(_C[i,1]-_C[j,1])/(xmax-xmin)<(length(cat(convert(_C[i,1],string),convert(_C[i,2],string)))+3)/60 and abs(_C[i,2]-_C[j,2])/(ymax-ymin)<0.05 then
k:=k+1:
fi:
od:
if _C[i,2]=0 and k=0 then
A:={ABOVE,RIGHT}:
else
if _C[i,2]=0 and k>0 then
A:={ABOVE,LEFT}:
else
if k=0 then
A:={ABOVE,RIGHT}:
else
A:={BELOW,LEFT}:
fi:
fi:
fi:
if r1=true then
B:="minimale"
else
B:="maximale"
fi:
g[i]:=plots[textplot]([_C[i,1],_C[i,2],cat(" (",convert(_C[i,1],string),", ",convert(_C[i,2],string),") ")],align=A):
_t:=cat(`La valeur `, B, ` de la fonction objectif est `, convert(_w,string), ` lorsque `, convert(x,string), `=`, convert(c[1,1],string), ` et `, convert(y, string), `=`, convert(c[1,2],string), ` ou lorsque `, convert(x,string), `=`, convert(c[2,1],string), ` et `, convert(y, string), `=`, convert(c[2,2],string), ` ainsi que tous les points sur le segment joignant les deux solutions.`):
od:
fi:
_sr:=plots[display]([g1,seq(g[i],i=1..nops(_C)),g2], view=[1.2*xmin .. 1.2*xmax, 1.2*ymin .. 1.2*ymax], labels=[x, y], font=[HELVETICA,9], tickmarks=[0,0]):
_sr
else
if s_opt={} then
g2:=plots[textplot]([0,0,""]):
_t:=cat(`Il n'y a pas de solution optimale car l'ensemble`, `\134n`, `des SOLUTIONS REALISABLES est VIDE.`):
_sr:=plots[display]([g1,g2], labels=[x, y], font=[HELVETICA,9], tickmarks=[0,0]):
_sr
else
if s_opt=NULL then
g2:=plots[textplot]([0,0,""]):
_t:=cat(`La solution n'existe pas car l'ensemble`, `\134n`, `des SOLUTIONS REALISABLES est NON BORNE.`):
_sr:=plots[display]([g1,g2], labels=[x, y], font=[HELVETICA,9], tickmarks=[0,0]):
_sr
fi:
fi:
fi:
else
if r1=true then
B:="minimale":
else
B:="maximale":
fi:
g1:=plot(0,x=1..10,1..10,axes=NONE):
if s_opt={} or s_opt=NULL then
if simplex[feasible](_cnsts, NONNEGATIVE)=true then
_t:=cat(`Il n'y a pas de solution. L'ensemble des SOLUTIONS REALISABLES est NON BORNE.`)
else
_t:=cat(`Il n'y a pas de solution. L'ensemble des SOLUTIONS REALISABLES est VIDE.`)
fi:
else
_t:=cat(`La valeur `, B, ` de la fonction objectif est `, convert(subs(s_opt,_obj),string), ` lorsque `, seq(cat(convert(s_opt[i],string),` , `),i=1..nops(s_opt)))
fi:
_sr:=plots[display](g1, labels=[x, y], font=[HELVETICA,9], tickmarks=[0,0]):
fi
else
g1:=plot(0,x=1..10,1..10,axes=NONE):
_t:=``:
_sr:=plots[display](g1, labels=[x, y], font=[HELVETICA,9], tickmarks=[0,0]):
fi:
if _nv=3 then
Maplets:-Tools:-Set('LB1'(caption)="Pour changer l'angle de vue, cliquez sur le graphique tout en faisant glisser la souris."):
x:='x': y:='y': z:='z':
for i from 1 to 3 do
if _var[i]="x" then
_var[i]:=_var[1]:_var[1]:="x"
elif _var[i]="y" then
_var[i]:=_var[2]:_var[2]:="y"
elif _var[i]="z" then
_var[i]:=_var[3]:_var[3]:="z"
fi
od:
x:=parse(op(1,_var)):
y:=parse(op(2,_var)):
z:=parse(op(3,_var)):
if s_opt<>{} and is(_obj,numeric)=false then
dim3(r1):
k:=[]:
for i from 1 to nops(_sommets) do
if subs({x=op(1,_sommets[i]),y=op(2,_sommets[i]),z=op(3,_sommets[i])},_obj)=v_opt then
k:=[op(k),_sommets[i]]
fi
od:
if k<>[] then
if nops(k)=1 then
j:=``
elif nops(k)=2 then
j:=`ainsi que tous les points sur l'ARETE du POLYEDRE CONVEXE contenant les deux solutions.`
elif nops(k)>=3 then
j:=`ainsi que tous les points sur la face du POLYEDRE CONVEXE contenant les solutions.`
fi:
if nops(k)>=1 then
_t:="":
_t:=cat(`La valeur `, B, ` de la fonction objectif est `, convert(parse(convert(v_opt,CaractDec)),string), ` si\134n`, seq(cat(convert(_t,string), convert(x,string), ` = `, convert(op(1,op(i,k)),string), `, `, convert(y,string), ` = `, convert(op(2,op(i,k)),string), `, `, convert(z,string), ` = `, convert(op(3,op(i,k)),string), `\134n`), i=1..nops(k)), j)
fi
fi
fi:
if is(_obj,numeric)=false then
Set('TB1'=convert(_t,string))
fi:
_sr
else
Set('TB1'=convert(_t,string)):
if _nv=2 then
_sr
elif _nv>3 then
_sr:=plots[textplot]([-1,0,`Aucune repr\303\251sentation possible`], axes=NONE)
fi
fi:
end use:
end:
dim3:=proc(r1)
local i, j, k, substituer, sommets, xmin, xmax, ymin, ymax, zmin, zmax, sm, eqs, s, r, p, S, g1, g2, g3, g4, X, pt, pl, ft, ct, eq, st, l:
global s_opt, v_opt, _obj, _cnsts, _sr, _sommets:
_sommets:='_sommets':
_cnsts := _cnsts union { x >= 0, y >= 0 , z >= 0, x<=1000000000, y<=1000000000, z<=1000000000}:
v_opt:=subs(s_opt,_obj):
s_opt:=[seq([subs([s_opt][i], x ), subs([s_opt][i], y ), subs([s_opt][i], z )], i=1..nops([s_opt]))]:
eqs:={seq(convert(_cnsts[i],equality),i=1..nops(_cnsts))}:
_sommets:=[]:
for i from 1 to nops(eqs) do
for j from i+1 to nops(eqs) do
for k from j+1 to nops(eqs) do
_sommets:=[op(_sommets),solve({eqs[i],eqs[j],eqs[k]})]
od
od
od:
s:=_sommets:
_sommets:=[seq([subs(_sommets[i], x ), subs(_sommets[i], y ), subs(_sommets[i], z )], i=1..nops(_sommets))]:
p:=[]:
for i from 1 to nops(_sommets) do
substituer:=subs(convert(op(i,s),set), convert(_cnsts,list)):
k:=0:
for j from 1 to nops(substituer) do
if is(op(j,substituer))=true then
k:=k+1
fi
od:
if k=nops(_cnsts) then
p:=[op(p),op(i,_sommets)]
fi:
od:
p:=convert(convert(p,set),list):
_sommets:=p:
s:=[]:
for i from 1 to nops(_sommets) do
for j from i+1 to nops(_sommets) do
for k from j+1 to nops(_sommets) do
s:=[op(s),[_sommets[i],_sommets[j],_sommets[k]]]
od
od
od:
pt:=[]:
for i from 1 to nops(s) do
pt:=[op(pt),[seq(add(op(k,op(j,op(i,s))),j=1..3),k=1..3)/3]]
od:
pl:=[]:
for i from 1 to nops(pt) do
pl:=[op(pl),[subs({x=op(1,op(i,pt)), y=op(2,op(i,pt)), z=op(3,op(i,pt))},convert(_cnsts,list))]]
od:
ft:=[]:
for i from 1 to nops(pl) do
ct:=0:
for j from 1 to nops(op(i,pl)) do
for k from 1 to nops(op(j,op(i,pl))) do
if is(convert(op(k,op(j,op(i,pl))),equality))=false then
ct:=ct+1
fi
od
od:
if ct<nops(_cnsts) then
ft:=[op(ft),op(i,s)]
fi
od:
ft:=convert(convert(ft,set),list):
eq:=[]:
for i from 1 to nops(ft) do
eq:=[op(eq),plan(seq(op(j,op(i,ft)),j=1..nops(op(i,ft))))]
od:
for i from 1 to nops(eq) do
for j from i+1 to nops(eq) do
if is(eq[i]+eq[j])=true then
eq[j]:=eq[i]
fi
od
od:
eq:=convert(convert(eq,set),list):
for i from 1 to nops(eq) do
st[i]:=[]:
for j from 1 to nops(_sommets) do
if is(subs({x=op(1,_sommets[j]),y=op(2,_sommets[j]),z=op(3,_sommets[j])},eq[i]))=true then
st[i]:=[op(st[i]),[op(1,_sommets[j]),op(2,_sommets[j]),op(3,_sommets[j])]]
fi
od
od:
st:=[seq(st[i],i=1..nops(eq))]:
st:=convert(convert(st,set),list):
sm:=[]:
for l from 1 to nops(st) do
for i from 1 to nops(op(l,st)) do
for j from i+1 to nops(op(l,st)) do
for k from j+1 to nops(op(l,st)) do
sm:=[op(sm),[op(i,op(l, st)), op(j,op(l, st)), op(k,op(l, st))]]
od
od
od
od:
sm:=op(convert(convert(sm,set),list)):
sommets:=[]:
for i from 1 to nops(_sommets) do
if op(1,op(i,_sommets))<1e6 and op(2,op(i,_sommets))<1e6 and op(3,op(i,_sommets))<1e6 then
sommets:= [op(sommets),op(i,_sommets)]
fi
od:
if max(seq(op(1,sommets[i]),i=1..nops(sommets))) = 0 then
xmax:=5
else
xmax:=max(seq(op(1,sommets[i]),i=1..nops(sommets)))
fi:
if max(seq(op(2,sommets[i]),i=1..nops(sommets))) = 0 then
ymax:=5
else
ymax:=max(seq(op(2,sommets[i]),i=1..nops(sommets)))
fi:
if max(seq(op(3,sommets[i]),i=1..nops(sommets))) = 0 then
zmax:=5
else
zmax:=max(seq(op(3,sommets[i]),i=1..nops(sommets)))
fi:
for j from 1 to nops(_sommets) do
X[j]:=[seq(op(i,op(j,_sommets)),i=1..nops(op(j,_sommets)))]
od:
r:=eqs minus {x = 1000000000, y = 1000000000, z = 1000000000}:
for i from 1 to nops(eqs) do
for j from i+1 to nops(eqs) do
if is(eqs[i]+eqs[j])=true then
r:=r minus {eqs[i]}
fi:
od:
od:
eqs:=r:
r:=[]:
for i from 1 to nops(_sommets) do
for j from i+1 to nops(_sommets) do
l:=0:
for k from 1 to nops(eqs) do
if is(subs({x=(op(1,op(i,_sommets))+op(1,op(j,_sommets)))/2, y=(op(2,op(i,_sommets))+op(2,op(j,_sommets)))/2, z=(op(3,op(i,_sommets))+op(3,op(j,_sommets)))/2},op(k,eqs)))=true then
l:=l+1:
fi:
od:
if l>1 and op(i,_sommets)<>op(j,_sommets) then
r:=[op(r),[op(i,_sommets),op(j,_sommets)]]
fi:
od:
od:
r:=convert(convert(convert(r,set),set),list):
g1:=plots[textplot3d]([seq([seq(op(i,op(j,_sommets)),i=1..nops(op(j,_sommets))), X[j]], j=1..nops(_sommets))], color=black, font=[HELVETICA, 9]):
i:=simplex[minimize](x+y+z,_cnsts minus {x<=1000000000, y<=1000000000, z<=1000000000},NONNEGATIVE):
j:=simplex[maximize](x+y+z,_cnsts minus {x<=1000000000, y<=1000000000, z<=1000000000},NONNEGATIVE):
if is(subs(i,_obj)<infinity) and is(subs(j,_obj)<infinity) then
if s<>[] or op(r)<>[] then
PLOT3D(POLYGONS(sm), STYLE(PATCHNOGRID), COLOR(XYZSHADING), LIGHT(0,0,0.0,0.1,0.0), LIGHT(100,45,0.1,0.0,0.0),LIGHT(100,-45,0.0,0.0,0.1), AMBIENTLIGHT(1,1,1)):
PLOT3D(POLYGONS(op(r)),STYLE(PATCH)):
g2:=plots[display]([%,%%]):
else
g2:=PLOT3D(POLYGONS([[subs(i, x ), subs(i, y ), subs(i, z )],[subs(j, x ), subs(j, y ), subs(j, z )]]), STYLE(PATCH), COLOR(ZHUE)):
fi:
else
xmax:=2*xmax:
ymax:=2*ymax:
zmax:=2*zmax:
PLOT3D(POLYGONS(sm), STYLE(PATCHNOGRID)):
PLOT3D(POLYGONS(op(r)),STYLE(PATCH)):
g2:=plots[display]([%,%%]):
fi:
if is(v_opt<infinity)=true then
if is(subs(z='a',_obj)=_obj)=true then
k:=_obj+(1e-3)*z:
else
k:=_obj
fi:
i:=1.2:
while whattype(traperror(plot3d(solve(k=v_opt,z), x=-i*xmax..i*xmax, y=-i*ymax..i*ymax)))=string do
i:=i+.1:
od:
g3:=plot3d(solve(k=v_opt,z), x=-0.1*xmax..i*xmax, y=-0.1*ymax..i*ymax, transparency=0.80, shading=XY, style=PATCHNOGRID):
_sr:=plots[display]([g1,g2,g3], view=[-0.1*xmax..1.2*xmax,-0.1*ymax..1.2*ymax, -0.1*zmax..1.2*zmax], tickmarks=[0, 0, 0], axes=NORMAL, orientation=[-20, 65], labels=[x, y, z]):
else
_sr:=plots[display]([g1,g2], view=[-0.1*xmax..1.2*xmax,-0.1*ymax..1.2*ymax, -0.1*zmax..1.2*zmax], tickmarks=[0, 0, 0], axes=NORMAL, orientation=[-20, 65], labels=[x, y, z])
fi
end:
dRapide := proc(n)
local i, j, d, dl, db, dp, dr:
if n=1 then
d:=Maplets:-Tools:-Get('TF2')
else
d:=Maplets:-Tools:-Get('TF3')
fi:
if d<>"" then
if d[length(d)]<>"
" then
d:=cat(d,"
")
fi:
else
return
fi:
dl:=[]:
db:="":
dp:="":
for i from 1 to length(d) do
if (d[i]="." and dp<>".") or (d[i]="," and dp<>",") or (d[i]="-" and dp<>"-") or d[i]="0" or d[i]="1" or d[i]="2" or d[i]="3" or d[i]="4" or d[i]="5" or d[i]="6" or d[i]="7" or d[i]="8" or d[i]="9" or d[i]="/" or d[i]="*" then
db:=cat(convert(db,string),convert(d[i],string)):
dp:=d[i]:
elif d[i]=" " then
db:=cat(convert(db,string),","):
elif db<>"" and d[i]="\134n" then
if whattype(traperror(parse(db)))=string then
if n=1 then
j:="de la fonction objectif."
else
j:="des contraintes."
fi:
Maplets[Examples][Alert](cat("Erreur: coefficients ",j)):
return()
fi:
if (d[i]="\134n" and d[i-1]=",") or(d[i]<>" " and d[i-1]=" ") then
db:=cat("[",seq(db[k], k=1..length(db)-1),"]"):
dl:=[op(dl),parse(db)]:db:=""
else
db:=cat("[",convert(db,string),"]"):
dl:=[op(dl),parse(db)]:db:=""
fi
fi
od:
d:="":
dr:="":
for i from 1 to nops(dl) do
dr[i]:="":
for j from 1 to nops(dl[i])-1 do
dr[i]:=cat(convert(dr[i],string), `(`, convert(dl[i,j],string), `)`, `*x`, convert(j, string),`+`):
od:
if n=2 then
dr[i]:=parse(cat(convert(dr[i],string),`0<=`,convert(dl[i,j],string))):
else
dr[i]:=parse(cat(convert(dr[i],string), `(`, convert(dl[i,j],string), `)`, `*x`, convert(j, string))):
fi:
d:=cat(convert(d,string),convert(dr[i],string),`\134n`):
od:
convert(d,name)
end:
plan := proc(a,b,c)
local n,r:
global x,y,z:
n := linalg[crossprod](b-a,c-a):
r := vector([x,y,z]):
linalg[innerprod](n,r-a)=0:
end:
conserver:=proc()
local i, t:
global _cnsts, _obj, s_opt, _nv, _w:
use Maplets[Tools] in
print():
if Get('RB1')=true then
t:=`Minimiser `
else
t:=`Maximiser `
fi:
print(cat(t,convert(_obj,string))):
print(`soumise aux contraintes`):
_cnsts:=_cnsts minus {x<=1000000000, y<=1000000000, z<=1000000000}:
for i from 1 to nops(_cnsts) do
print(op(i,_cnsts))
od:
if _nv>3 then
print(`toutes les variables sont non n\303\251gatives.`)
fi:
if (_nv=2 or _nv=3) and s_opt<>{} and s_opt<>"" then
print(_sr)
fi:
print(_t):
print(__________________________________________________):
end use
end:
`convert/CaractDec`:= proc(x)
local X, i, j:
X:= sprintf(cat("%", 2*Digits+2, ".", Digits, "f"), x):
for i while X[i] = " " do od:
for j from length(X) by -1 while X[j] = "0" do od:
if X[j] = "." then j:= j-1 fi:
X[i..j]
end:
rep:= proc()
global _t:
_t
end:
with(Maplets[Elements]):
prog:=Maplet('onstartup'=RunWindow('W1'),
Window['A1'](title="Aide", 'layout' = 'BA0', height=430, width=600, resizable = false),
BoxLayout['BA0'](
BoxColumn(
TextBox['TB2'](height=18,editable=false,
"Cette application permet d'optimiser une fonction lin\303\251aire \303\240 deux variables ou plus, soumise \303\240 des contraintes de la forme
a*x+b*y+c*z ... <= d
a*x+b*y+c*z ... >= d
a*x+b*y+c*z ... = d
Lorsque le probl\303\250me est \303\240 deux ou \303\240 trois variables, l'application localise dans le plan cart\303\251sien ou dans un espace \303\240 trois dimensions, l'ensemble convexe des solutions r\303\251alisables du probl\303\250me ainsi que tous ses sommets. En faisant glisser la souris, on peut examiner sous tous les angles les espaces \303\240 trois dimensions.
Il n'est pas n\303\251cessaire d'indiquer les contraintes de non n\303\251gativit\303\251 du probl\303\250me ( x>=0, y>=0, z>=0, ... ), l'application s'en charge. Vous pouvez utiliser les variables de votre choix (x, y, z, u, v, t, x1, x2 ... ).
La fonction objectif et les contraintes du probl\303\250me peuvent \303\252tre entr\303\251es directement dans les cases correspondantes. Pour acc\303\251l\303\251rer l'entr\303\251e des donn\303\251es, cliquez sur \302\253Donn\303\251es simplifi\303\251es\302\273 en utilisant le menu \302\253Option\302\273 ou en utilisant le bouton droit de la souris avec le curseur plac\303\251 au pr\303\251alable sur une des cases contenant les donn\303\251es."
),
Button("FERMER",CloseWindow('A1'))
)
),
Window['W0'](title="Aide (donn\303\251es simplifi\303\251es)", 'layout' = 'BA1', height=420, width=360, resizable = false),
BoxLayout['BA1'](
BoxColumn(
TextBox['TB3'](height=18, editable=false, font=Font('Courier',12),
"Pour entrer le programme suivant:
Maximiser 3*x + 5*y
2*x - 5*y <= 7
x + 3*y >= 2
x >= 1
y <= 3
x >= 0
y >= 0
il faut d'abord pr\303\251senter toutes les contraintes du programme (sauf celles de non n\303\251gativit\303\251) sous la forme <=
Maximiser 3*x + 5*y
2*x - 5*y <= 7
-x - 3*y <= -2
-x <= -1
y <= 3
puis entrer les coefficients de la fonction objectif et des contraintes en utilisant la virgule comme s\303\251parateur.
3, 5
2,-5, 7
-1,-3,-2
-1, 0,-1
0, 1, 3"
),
Button("FERMER",CloseWindow('W0'))
)
),
Window['W1'](title="Programmation lin\303\251aire", 'menubar'='MB1', height=585, width = 785, 'layout' = 'BL1', resizable = false),
BoxLayout['BL1'](
BoxRow(
BoxColumn(border=true,
BoxRow(
RadioButton['RB1']("Minimiser", 'value'=false,'group'='BG1'),
RadioButton['RB2']("Maximiser", 'value'=true,'group'='BG1')
),
"la fonction objectif",
TextBox['TF0']('value' = "x+3*y+9*z", 'popupmenu'='PM1', height=3, width = 40, wrapped=false),
TextField['TBX']('value' = "", visible=false),
"soumise aux contraintes",
TextBox['TF1']('value' = "x+y+z <= 9\134nx >= 3\134n2*x-y+3*z <= 12", 'popupmenu'='PM2', height=12, width = 40, wrapped=false),
Button['B1']("R\303\251soudre", width=100, Action(SetOption('B1'(enabled)=false), SetOption('LB1'(caption)=""), SetOption('TB1'=""), Evaluate('PL1'= 'dStandard(RB1)'), SetOption('B1'(enabled)=true))),
BoxRow('inset'=0, 'spacing'=0,
Button("Conserver", width=100, Action(SetOption('target' = 'TB1', 'value'= ""), Evaluate('PL1'= 'dStandard(RB1)'), Evaluate('function' = 'conserver()'))),
Label(" ", font=Font('Helvetica',4)),
Button("Effacer", width=100, Action(SetOption('TF0' = ""),SetOption('TF1' = ""), SetOption('TB1' = ""), Evaluate('PL1'= 'plots[textplot]([0,0,""],axes=NONE)')))
),
Label("\302\251 Andr\303\251 L\303\251vesque", halign =left, font=Font('Helvetica',10))
),
BoxColumn('inset'=0, 'spacing'=0,
BoxRow('inset'=0, 'spacing'=0, border=true,
[Plotter['PL1'](height=375, width=375),
Label['LB1']("", font=Font('Helvetica',9))]
),
BoxRow( border=true,
TextBox['TB1']("", height=4, width=48)
)
)
),
MenuBar['MB1'](
Menu("Fichier",
MenuItem("Fermer", Shutdown())
),
Menu("Option",
MenuItem("Donn\303\251es simplifi\303\251es", onclick = Action(RunWindow('W2')))
),
Menu("?",
MenuItem("Aide", RunWindow('A1'))
)
)
),
ButtonGroup['BG1'](),
PopupMenu['PM1'](MenuItem("Donn\303\251es simplifi\303\251es", onclick = Action(RunWindow('W2'), SetOption('TF2'(focus)=true)))),
PopupMenu['PM2'](MenuItem("Donn\303\251es simplifi\303\251es", onclick = Action(RunWindow('W2'), SetOption('TF3'(focus)=true)))),
Window['W2'](title="Donn\303\251es simplifi\303\251es" , 'layout' = 'BL2', resizable = false),
BoxLayout['BL2'](
BoxColumn(
Label("Coefficients de la fonction objectif", font=Font('Helvetica',11)),
TextBox['TF2']("2,1", width=15, height=3, wrapped=false),
BoxRow(
Label(" Coefficients des contraintes \303\251crites sous la forme :", font=Font('Helvetica',11)),
Label(" <= ", font=Font('courier',12))
),
TextBox['TF3']("1,1,9\134n-3,-2,-6\134n1,0,5\134n0,1,6", width=15, height=10, wrapped=false),
BoxRow(
Button("Transf\303\251rer", width=100, onclick = Action( Evaluate('TF0'=""), Evaluate('TF1'=""), Evaluate('TB1'=""), Evaluate('PL1'= 'plots[textplot]([0,0,``], axes=NONE)'), Evaluate('TF0'='dRapide(1)'), Evaluate('TF1'='dRapide(2)'), SetOption('LB1'(caption)=""), CloseWindow('W2')))
),
BoxRow(
Button("Effacer", width=100, Action(SetOption('TF2' = ""),SetOption('TF3' = ""))),
Button("Aide", width=100, RunWindow('W0'))
)
)
)
):
Maplets[Display](prog);